Analysis To Several Predator-prey Systems With Impulsive Effect

Comparing with the classical diferential system, impulsive diferential equa-tions could describe the dynamical behavior of the system in more detail, in whichthe state change abruptly and is discontinuous at some moments. In recent years,the theory of impulsive diferential equations has been gradually used in populationecology. Based on the exploitation and utilization strategies of biological resourcesand efective management on pest, we study the population biology models withstage structure and impulsive efect. We obtain the sufcient conditions for sus-tainable exploitation and utilization of regenerate resources and efective controlpests.Firstly, we consider a predator-prey model with impulsive stocking fry andharvest fsh at diferent fxed moment. By using the comparison theorem of impulsivediferential equation, we get the sufcient condition that the number of stocking fryor the stocking periodic and the amount of harvesting fsh, which can ensure thesystem can be sustainable and we can get a lot of economic efciency. By usingMatlab, we numerical simulate the result’s reliability.Secondly, we investigate a Beddington-DeAngelis type prey-predator model, inwhich the prey has stage structure and both of the immature prey and the predatorhave impulsive efect. Using the comparison theorem, we get the sufcient conditionsfor the global attractivity of the prey-extinction periodic solution and permanenceof the system. Numerical simulations of Matlab are inset to verify the feasibility ofthe theoretic results.Finally, we discuss a Holling type Gomptorz prey-predator model with stage-structure and impulsive efect. Using stroboscopic map, we analyze the global attrac-tivity for the mature predator extinction periodic solution, and give the sufcientcondition for permanence of the system. Numerical simulations are presented toconfrm the feasibility of our theoretic results.